Where you'd like to stay in for as long as you desire. You get access to all of it's libraries and get all the time in the world to play every single one. What would it be?
Mine would actually have to be the Sixth Generation, the PS2/X-Box/GameCube/DC era. I almost wanted to say the Fifth Generation (PS1/N64/Saturn) but I had more fonder memories with 6th Gen than any other generation. My system of choice back then was the PS2, although I did have an X-Box on a couple occasions as well as a GameCube a couple times but they both just didn't stick with me as well as the PS2 did.
I loved the hell out of games like Twisted Metal: Black, WWE Smackdown!: Here Comes the Pain (Arguably the best wrestling game made), GTA III, God of War, Soul Calibur II, Kingdom Hearts (Only the first one) and many others. I liked how drenched the gaming industry felt at that time where the heat was really picking up and people were really into it. I think it's the last generation we'll know of that didn't have DLC and the microtransaction system in place either.
Stepping off from 5th Gen into 6th Gen gave me that "WOAH!" feeling because of the transitioning from polygon-like graphics into more of the mesh well-textured graphical capabilities. Only to know that things would get better from there.